Parasites in eggs are extremely rare.
In the extremely unlikely event that a parasite were present, it would be killed by cooking. Eggs should always be cooked until both the white and the yolk are firm—not runny. This kills any potential bacteria and parasites.
The chalaza is not a parasite. It’s not a worm. It’s a structural protein. You can eat it without worry.
A Quick Word on Food Anxiety
I’m going to be honest here.
I have a tendency to overthink food. I see something strange, my brain goes